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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 30
# Folio 10r, page id 00068243:0019
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v. octobu 167
promotus re
Arithmeticae diophant
habeae minorum rationatem, ita enim si
s
ratis seriibus ex quibjagnosci possit an aeiquatio data
preter datam aequationem
v. 9. X + V (3. adhnc aera supponatur
ut X + 6V + X + Y + C. p0. videndum in sufficiat una imognita sublata provenore aequationem
divisibilem sive rationalem ita emius ut s hoc loco fiet: X + y 1 - dy - C 113. Ergo erit yp, e+3
a
ergo sed ita substituendo non habebimus valorem ipsius X absoluto. Quod tamen ita assequemur si pro X faci
9+ b. fier Z + 2bZ + b + y 13. et
modo, qua non remaneerd Z.
eiit ergo
3V + 267 +6 +y  FdY + C 11. sed hoc inutilo; hoc
t
X +(3. C +bC7G
1 A1 Y3a2 = et -60 = 9
a
ergo debet 3d = e = 6C = 9 esse quadratus. quae difficultas est aequalis curo difficitor data
ergo aliter praeter aequationem X +y 3a ponamus X +Y + dY + cX +C1v.
i
d
fier
st
dy +
CX
+C  - 3.
+ 2d eV + 1d + C
+ 6.d.
aequatio
+b ea
9a2)
-
6a.
1
et X H - dy - e - 3a
)
bec 3- y
a
sive
=
d s - 64
d
= 6aY (F 9a). Quae aequatio videndum est an solvi possit
in numeris quem in finem faciumus
+
d
2 + 2d ba
+ 36a
d+ + 2d6a (+36a
4
CH- 3a
( 9a) a= 18a
4, 3a= (0
Co
crit
et deber dt + 2ba esse quadratue. quod  fieri potessi
sit ille _ d+ 2deo +co. fiet: 26ap 2 dco + co  et dp 364 434 = co
et fier
2
+ C0). et y 1)
A
a
cas
+ 3a 4
co
u
1594 - 8, 3a + Co
sed satis agnosio nos non multa hiecu
con
ducturos nisi quod
quaestionem propositam simplicem mulide poleriu en mide
ompositas quod dicissimi seroiet ad posilas rednebuda, ad simplicest.
sioner
Gene
vera methoiu redo, in eo consisteret. ut generalis fiait substitutio v.g. data aequalio est
+ 2
B
Xy
e
3. Fingatur aequatio: ed
dl
+ Xy
+ X
a- 1 1
Va-2
etc.
+
X.
c
 - 1
d
XC -2
o- 3
+ V2
sed satius ne in in infinitum rabeat
+ Y∞- 1
certuri
efigere gradum pro X+ quo X et V. summa aeq potestates aequalis sumuntur et fiet
Bat
N + XC
X P
X
-2
erc. et X. v
d
3-2
et X
X
X
β-1
81
ata ordine; porento quaslibet mulliplicati, excepto. uno y. quod mulo affectum, quia
calculum explicationios explicabimus generalem.
4
Y-2
(3-7 2
a
(